PreprintCC0arXiv
Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length
Abstract
We prove a large deviation principle for the area of a two-pointed weight-W quantum disk conditioned to have left boundary length one, where 0<W<2 is fixed and γ↓0 without a subsequence restriction. Conformal welding and the one-block mating-of-trees law give independent Brownian blocks and a recursive area decomposition. Growing moments and negative Laplace transforms lead to two Hamilton--Jacobi equations, whose characteristic solutions determine the limiting transforms. Direct comparison proves moment convergence; compact-interval comparison and a change of measure prove Laplace convergence. The resulting good rate function is specified by scalar endpoint equations and is elementary when W=1.
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BibTeX
@misc{fan2026large,
title = {{Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length}},
author = {Yuchen Fan and Zhenfeng Tu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02531},
eprint = {2610.02531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02531},
note = {CC0},
}
RIS
TY - UNPB
TI - Large Deviation Principles for Area of Quantum Disks with Unit Left Boundary Length
AU - Yuchen Fan
AU - Zhenfeng Tu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02531
UR - https://arxiv.org/abs/2610.02531
AB - We prove a large deviation principle for the area of a two-pointed weight-W quantum disk conditioned to have left boundary length one, where 0<W<2 is fixed and γ↓0 without a subsequence restriction. Conformal welding and the one-block mating-of-trees law give independent Brownian blocks and a recursive area decomposition. Growing moments and negative Laplace transforms lead to two Hamilton--Jacobi equations, whose characteristic solutions determine the limiting transforms. Direct comparison proves moment convergence; compact-interval comparison and a change of measure prove Laplace convergence. The resulting good rate function is specified by scalar endpoint equations and is elementary when W=1.
ER -